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A novel nonlinear fractional order damped Pantographs equation involving input delay is formulated. We explored the controllability of the underlying nonlinear damped dynamical Pantograph equation of fractional order with input delay. The solution of the problem under consideration has initially expressed in the form of the Mittag–Leffler function in two different domains. The controllability Grammians matrices for both cases have been defined. Controllability in the linear case has been shown and applied Schaefer’s fixed point theorem as well as the Arzela-Ascoli theorem to derive necessary conditions for the controllability of the nonlinear case.

In this paper, we investigate gross domestic product model with four different fractional derivatives. We find the solutions of fractional models by utilizing Sumudu transform. We prove the efficiency of the Sumudu transform by some theoretic outcomes and applications. We demonstrate the simulations by some figures. We show the agreement of different fractional derivatives on the model.

The nanofluid technology has added significant contributions towards heat exchange increase and decrease in energy loss. This article focuses, to analyze the heat and mass transfer for two distinct hybrid nanofluids, namely (Ag-CuO/NE), (Ag-CuO/SE), under the impact of magnetic field and Rosseland radiation over a rotating cone embedded in the porous medium. The set of non-linear partial differential equations is derived with help of boundary layer approximation. A suitable and appropriate similarity set is used to obtain a dimensionless set of equations which, are then converted into ordinary differential equations. The problem is tackled numerically with the BVP-4c technique, keeping tolerance at 10−06. The influence of flow study parameters is discussed with help of graphical and tabulated data. The study shows that (Ag-CuO/NE) hybrid nanofluid has produced better heat and mass transfer rates as compared (Ag-CuO/SE) hybrid nanofluid. Therefore, the study suggests more frequent use of (Ag-CuO/NE).

Up to day, the role of ultraviolet rays in producing cancers like melanoma has been considered extensively. However, quantum effects on the evolutions of melanoma has been discussed minorly. In this research, we propose a quantum model for the replication of DNAs within skin cells. We show that ultraviolet rays prevent of imaging information within genes of parent cells on genes of child cells and make some genetic errors in produced DNAs during replications. We compare the model with experimental data and obtain the growth rate of tumour on the skin.

In this work, a nonlinear integral resonant controller is utilized for the first time to suppress the principal parametric excitation of a nonlinear dynamical system. The whole system is modeled as a second-order nonlinear differential equation (i.e., main system) coupled to a nonlinear first-order differential equation (i.e., controller). The control loop time-delays are included in the studied model. The multiple scales homotopy approach is employed to obtain an approximate solution for the proposed time-delayed dynamical system. The nonlinear algebraic equation that governs the steady-state oscillation amplitude has been extracted. The effects of the time-delays, control gain, and feedback gains on the performance of the suggested controller have been investigated. The obtained results indicated that the controller performance depends on the product of the control and feedback signal gains as well as the sum of the time-delays in the control loop. Accordingly, two simple objective functions have been derived to design the optimum values of the loop-delays, control gain, and feedback gains in such a way that enhances the efficiency of the proposed controller. The analytical and numerical simulations illustrated that the proposed controller could eliminate the system vibrations effectively at specific values of the control and feedback signal gains. In addition, the selection method of the loop-delays that either enhances the control performance or destabilizes the system motion has been explained in detail.

Partial differential equations are among the most important mathematical tools for scientists in describing many physical and engineering problems related to real life. Accordingly, in this work, an efficient technique is proposed for getting different collections of solutions to a third-order version of nonlinear Schrödinger's equation. Some numerical simulations related to the acquiblack solutions are also provided in this research. All results presented in this article can be consideblack as new achievements for the model. Further, it is emphasized that the used technique enables us to study other forms of nonlinear models. It is obtained that the technique is a reliable tool in handling many nonlinear partial differential equations arising in engineering, fluid mechanics, nonlinear optics, oceans, seas, and many mathematical physics. Moreover, the present results help the plasma physics researchers for investigating many nonlinear modulated structures that can generate and propagate in laboratory and space plasmas. © 2022 The Authors

In this article, we investigated a deterministic model of pneumonia-meningitis coinfection. Employing the Atangana–Baleanu fractional derivative operator in the Caputo framework, we analyze a seven-component approach based on ordinary differential equations (DEs). Furthermore, the invariant domain, disease-free as well as endemic equilibria, and the validity of the model’s potential results are all investigated. According to controller design evaluation and modelling, the modulation technique devised is effective in diminishing the proportion of incidences in various compartments. A fundamental reproducing value is generated by exploiting the next generation matrix to assess the properties of the equilibrium. The system’s reliability is further evaluated. Sensitivity analysis is used to classify the impact of each component on the spread or prevention of illness. Using simulation studies, the impacts of providing therapy have been determined. Additionally, modelling the appropriate configuration demonstrated that lowering the fractional order from 1 necessitates a rapid initiation of the specified control technique at the largest intensity achievable and retaining it for the bulk of the pandemic’s duration.

This paper focuses on studying thermal, elastic and coupled plasma waves, in the sense of a photo-thermal process transport within an infinite semiconductor medium. In order to study photo-thermal interactions in two-dimensional semiconducting materials, a new mathematical model based on the Moore–Gibson–Thompson equation (MGTE) is implemented. The MGTE model involving the Green–Naghdi model of type III as well as the heat transport equation proposed by Lord and Shulman. We consider the semi-conductor half-space is rotated at a uniform angular speed and magnetized. The analysis of the distribution of thermophysical fields has been extracted by a normal mode method, represented graphically and discussed. The results predicted by the new and improved model have been compared with the generalized and classic ones. In addition, all field quantities have been examined for effects of rotation, a lifetime of the photo-generated, and the applied magnetic field.

The main purpose of the present paper is to introduce a reliable method, for the first time, in solving differential equations with partial derivatives. The significant idea behind this method is the modification of a well-known method. The main base functions used in the solution's structures are Jacobi elliptic functions which are known functions and have many applications in practice. In order to achieve these results, the perturbed Schrödinger equation with Kerr law nonlinearity is considered. This nonlinear equation illustrates the propagation of optical solitons in nonlinear optical fibers. Thereupon, several analytical solutions corresponding to this model are obtained through employing an improved generalized exponential rational function method. Then we present a new version of it that is presented for the first time in the literature. Using these methods, several wave solutions related to the considered model are obtained. Moreover, several numerical simulations relevant to the resulting solutions are performed in the paper. As a notable features of the proposed method, the obtained solutions are characterized by the Jacobi elliptic functions. These solutions contain an index that for some specific choices is reduced to standard functions such as trigonometric and hyperbolic. The obtained results and solutions can be used for investigating the mechanism of several nonlinear phenomena laboratory and space plasmas. All necessary calculations are performed via symbolic packages of Wolfram Mathematica. © 2022 The Authors

New definitions always have more capabilities in describing phenomena than the more classic and well-known concepts because they usually appear to fill the gaps in existing concepts. In this paper, we employ a new stochastic fractional system that models interactions in a mutualism–parasitism food web. The main idea of piece-wise differential and integral operators is to separate the time under study into separate time domains in which the model behaves different behaviors. The idea was recently proposed by Atangana et al., and is gradually being used to solve a variety of application models. In order to demonstrate the valuable capabilities of this approach, many numerical simulations are provided in this paper. These results are mainly obtained from studying the role of the parameters in the model on its overall behavior. The results confirm that the piece-wise approach to the problem is a wise idea with more effectiveness rather than considering the whole situation is studied by a single operator. It is recommended to use these modified operators in modeling other applied problems with similar features.

Infectious diseases are the major source of increasing death rate during recent years. Among the infectious diseases, dengue fever is disseminated in more than hundred countries, especially in tropical and subtropical regions. In this work, a novel fractional model is presented which describes the dynamics of dengue including human and vector (mosquitoes) population. The mathematical model of dengue transmission is important to understand the dynamical behavior of the disease. A compartmental model of the dengue transmission is composed of five compartments representing the human and mosquito dynamics. The model is solved by using Adams-Bashforth-Moulton technique. The simulated results are compared with four years (2011–2014) real time data of dengue cases in Lahore, Pakistan. The fractional model gives a better approximation for α = 0.8 as compared to α = 1. The reasonable range of fractional order is between α = 0.7 and α = 1. The stability analysis of the equilibria is presented. Moreover, the positivity of the solution is proved. Furthermore, the parametric study using the outbreak dengue data for Lahore is presented. On the basis of results, we conclude that the fractional order model is more suitable than integer order equations to evaluate the transmission of dengue disease. The present study plays an important role in studying the factors to remove the communicable diseases like dengue.

This comparative study inspects the heat transfer characteristics of magnetohydrodynamic (MHD) nanofluid flow. The model employed is a two-phase fluid flow model. Water is utilized as the base fluid, and zinc and titanium oxide (Zn and TiO2) are used as two different types of nanoparticles. The rotation of nanofluid is considered along the z-axis, with velocity ω*. A similarity transformation is used to transform the leading structure of partial differential equations to ordinary differential equations. By using a powerful mathematical BVP-4C technique, numerical results are obtained. This study aims to describe the possessions of different constraints on temperature and velocity for rotating nanofluid with a magnetic effect. The outcomes for the rotating nanofluid flow and heat transference properties for both types of nanoparticles are highlighted with the help of graphs and tables. The impact of physical concentrations such as heat transference rates and coefficients of skin friction are examined. It is noted that rotation increases the heat flux and decreases skin friction. In this comparative study, Zn-water nanofluid was demonstrated to be a worthy heat transporter as compared to TiO2-water nanofluid.

The industrial Internet of Things (IIoT) enables the interconnection of machines, devices, resources, and computing technologies to improve the reliability of manufacturing services. The role of Software-Defined Networks (SDNs) and Network Function Virtualization (NFV) are exploited in the IIoT environment to ensure effective management and computing resource utilization. Based on the SDN and NFV paradigms, this article introduces a novel elastic computing resource virtualization (ECRV) method to improve the flexibility of resource management in the IIoT. The need for virtualization is obtained by identifying the control and process platforms used in industrial task management. Support vector machine-based classification learning is used to achieve balanced identification, and prevents unnecessary distribution of limited resources, Support vector machine helps to retain flexibility in task control processes that use available industrial resources. By separating the process and control platforms, service dissemination is improved and backlogs in task processing are decreased. The proposed method could provide flexible virtualization and reduces the service response time and task failure.

In this paper, we will propose a novel system for remote detecting COVID-19 patients based on artificial intelligence technology and internet of things (IoT) in order to stop the virus spreading at an early stage. In this work, we will focus on connecting several sensors to work together as a system that can discover people infected with the Coronavirus remotely, this will reduce the spread of the disease. The proposed system consists of several devices called smart medical sensors such as: pulse, thermal monitoring, and blood sensors. The system is working sequentially starting by pulse sensor and end by blood sensor including an algorithm to manage the data given from sensors. The pulse sensor is devoted to acquire a high quality data using a smartphone equipped by a mobile dermatoscope with 20× magnification. The processing is used RGB color system to perform moving window to segment regions of interest (ROIs) as inputs of the heart rate estimation algorithm. The heart rate (HR) estimation is then given by computing the dominant frequency by identifying the most prominent peak of the discrete Fourier transform (DFT) technique. The thermal monitoring is used for fever detection using a smart camera that can provide an optimum solution for fever detection. The infrared sensor can quickly measure surface temperature without making any contact with a person’s skin. A blood sensor is used to measure percentages of white, red blood (WBCs, RBCs) volume and platelets non-invasively using the bioimpedance analysis and independent component analysis (ICA). The proposed sensor consists of two electrodes which can be used to send the current to the earlobe and measure the produced voltage. A mathematical model was modified to describe the impedance of earlobe in different frequencies (i.e., low, medium, and high). The COMSOL model is used to simulate blood electrical properties and frequencies to measure WBCs, RBCs and Platelets volume. These devices are collected to work automatically without user interaction for remote checking the coronavirus patients. The proposed system is experimented by six examples to prove its applicability and efficiency.

We introduce entangled pair coherent states of a noncommutative harmonic oscillator operators associated with a q-deformed oscillator algebra. The definition of two-mode q-deformed operator and the decomposition of its eigenstates in terms of the q-deformed Fock states are obtained. The general solution of the recurrence relation of the first nondeformed quadrature is obtained. The asymptotic behavior of the general solution is studied, a complete expansion is derived, and also representations of the general solution in terms of the Gauss hypergeometric function are given. Also, we prove that the general solution is related to Meixner-Pollaczek orthogonal polynomial and calculate the weight function. The photons number distribution, the second order correlation function and the optical tomogram of the entangled pair coherent states are discussed. The recurrence relation for the first q-deformed quadrature is inferred. We evaluate the eigenstate of the q-deformed quadrature operator and give a numerical study for the optical tomogram of the q-deformed of the entangled pair coherent states. Finally, we show the change of the parameters in the entangled pair coherent states that connected with physical quantities and explain how they affect the format of optimal tomography.